// https://www.acwing.com/problem/content/872/

#include <iostream>
#include <map>
using namespace std;

int MOD = 1e9+7;

// 对 n 进行质因数分解，结果存入 factors（传引用）
void primeFactorize(int a, map<int, int>& factors) {
    for (int d = 2; d <= a / d; ++d) {
        while (a % d == 0) {
            factors[d]++;
            a /= d;
        }
    }
    if (a > 1) {
        factors[a]++;
    }
}

int main() {
    int n, a;
    scanf("%d", &n);

    map<int, int> totalFactors; // 记录每个质因子的总指数

    for (int i = 0; i < n; ++i) {
        scanf("%d", &a);
        primeFactorize(a, totalFactors);
    }

    long long result = 1;
    for (auto& [prime, exp] : totalFactors) {
        result = result * (exp + 1) % MOD;
    }

    printf("%lld\n", result);

    return 0;
}